Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
824 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 292 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23782820 | C3 | semidirect |
| 3. #23782819 | C3 | semidirect |
| 4. #23782818 | C3 | semidirect |
| 5. #23782817 | C3 | semidirect |
| 6. #23782812 | C3 | semidirect |
| 8. #23782792 | C3 | semidirect |
| 9. 3−1+2×C43⋊C9 | C3 | semidirect |
| 10. #23782779 | C3 | semidirect |
| 22. #16812500 | C32 | semidirect |
| 23. #16812499 | C32 | semidirect |
| 24. (C43⋊C9)⋊C9 | C32 | semidirect |
| 25. (C43⋊C9)⋊C9 | C32 | semidirect |
| 26. (C43⋊C9)⋊C9 | C32 | semidirect |
| 30. C9×C43⋊C9 | C32 | semidirect |
| 43. C3×C43⋊C9 | 3−1+2 | semidirect |
| 120. C43 | #10624872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C43⋊C9 | 3 |
| #23782820 | 3 |
| #23782819 | 3 |
| #23782818 | 3 |
| #23782817 | 3 |
| #23782812 | 3 |
| #23782798 | 3 |
| #23782792 | 3 |
| 3−1+2×C43⋊C9 | 3 |
| #23782779 | 3 |
| C43×#6891 | 3 |
| #10624872 | 43 |